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comment L2 Matrix Norm Upper Bound in terms of Bounds of its Column
you do have the inequality $||A||_2\leq||A||_F$. Furthermore this inequality is tight if $A$ is rank 1 or less, so I'm not sure you will be able to find a better bound without further information.
Feb
3
comment Prove that if $X$ is subgaussian, then ${\bf E}e^{tX}=1+\sum_{k=1}^{\infty}\frac{t^k}{k!}{\bf E}X^k$
@A.S. no restrictions on $X$ because we can always set the interval to be $[0,0]$ correct?
Feb
3
comment Prove that if $X$ is subgaussian, then ${\bf E}e^{tX}=1+\sum_{k=1}^{\infty}\frac{t^k}{k!}{\bf E}X^k$
@A.S. ah! well I stand corrected.
Feb
3
comment Prove that if $X$ is subgaussian, then ${\bf E}e^{tX}=1+\sum_{k=1}^{\infty}\frac{t^k}{k!}{\bf E}X^k$
@A.S. To be honest I couldn't follow all of Arash's integral manipulations (which is why I provided my own solution once I came up with it), but I feel that subgaussianity (or at least sub-exponential tails) must be required for $\int_{\bf R}\exp(|tx|)d\mu_X$ to have any hope of existing.
Feb
2
comment Value of $\lim_{h\rightarrow 0}\frac{a^h-1}{h}$
use difference of powers to expand the numerator
Feb
2
comment How to integrate with a matrix in the measure?
well you really just need to figure out what is meant by the notation $d^{2n}M$, maybe it's defined in your book or your professor's notes or something.
Feb
2
comment How to integrate with a matrix in the measure?
I don't know enough about physics to answer this, but $\text{tr}(M^k)=\sum_i\lambda_i^k$, so if you treat $d^{2n}M$ as just $d\lambda_1...d\lambda_n$ or the equivalent for real and complex parts, you might be able to break the integral up into a product of integrals.
Jan
30
comment Sub-Gaussian Random Variable with Small Variance
you introduce epsilon but then do nothing with it.
Jan
25
comment Is dot product defined for matrices for other than terms being $n \times 1$ or $1 \times n$ vectors?
the dot product doesn't produce vectors it produces scalars.
Jan
21
comment Calculus: tricky integration problem.
you're overthinking this, there are many $g(x)$ which will work, all you need to do is find one. Use the fact that you can pull constants outside the integral.
Jan
21
comment Calculus: tricky integration problem.
consider $f(x) = (x^3-x)g(x)$, and now figure out what $g(x)$ could be.
Jan
13
comment Is $\log \det \left( I + \frac 1 {\sigma^2} H F \bar H \right)$ concave?
you mean the conjugate transpose?
Jan
13
comment Is $\log \det \left( I + \frac 1 {\sigma^2} H F \bar H \right)$ concave?
what is $\bar{H}$?
Jan
13
comment Solution of quadratic optimization with linear constraints
probably Lagrange multipliers then
Jan
13
comment Solution of quadratic optimization with linear constraints
are you expected to solve it analytically? or is this a specific problem with numerical values?
Jan
13
comment The differential of a symmetric matrix in terms of its eigen-decomposition
you're right that is interesting, but is there a way to use it to prove the formula above?
Jan
13
comment The differential of a symmetric matrix in terms of its eigen-decomposition
@user1952009, as far as I can tell this doesn't get me anything new.
Jan
12
comment Reference on properties of binary random vectors
This isn't really about random matrices. We're going to need to know more about exactly what you're looking for, as it stands what you're asking for is too broad and vague. Random vectors are just n-variate random variables and they are basically studied everywhere in probability and statistics.
Jan
6
comment Non Zero Function .Differomophism.
because $Df$ is linear and invertible it's an isomorphism of groups and thus must take the identity to identity.
Jan
6
comment Could someone offer an explanation of $x^{10} \equiv 1 \pmod{11}$?
look up Fermat's Little Theorem.